Base field \(\Q(\sqrt{114}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 114\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[3, 3, w]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $72$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 23x^{4} + 152x^{2} - 236\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -3w - 32]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 3]$ | $-e$ |
| 7 | $[7, 7, -w + 11]$ | $-\frac{1}{4}e^{4} + \frac{13}{4}e^{2} - \frac{13}{2}$ |
| 7 | $[7, 7, w + 11]$ | $-\frac{1}{4}e^{4} + \frac{13}{4}e^{2} - \frac{13}{2}$ |
| 11 | $[11, 11, w + 2]$ | $-\frac{1}{8}e^{5} + \frac{17}{8}e^{3} - \frac{29}{4}e$ |
| 11 | $[11, 11, w + 9]$ | $\phantom{-}\frac{1}{8}e^{5} - \frac{17}{8}e^{3} + \frac{29}{4}e$ |
| 13 | $[13, 13, w + 6]$ | $\phantom{-}\frac{3}{8}e^{4} - \frac{43}{8}e^{2} + \frac{47}{4}$ |
| 13 | $[13, 13, w + 7]$ | $\phantom{-}\frac{3}{8}e^{4} - \frac{43}{8}e^{2} + \frac{47}{4}$ |
| 19 | $[19, 19, w]$ | $-\frac{1}{4}e^{4} + \frac{9}{4}e^{2} + \frac{3}{2}$ |
| 37 | $[37, 37, w + 15]$ | $-\frac{1}{8}e^{4} + \frac{25}{8}e^{2} - \frac{53}{4}$ |
| 37 | $[37, 37, w + 22]$ | $-\frac{1}{8}e^{4} + \frac{25}{8}e^{2} - \frac{53}{4}$ |
| 41 | $[41, 41, 37w + 395]$ | $\phantom{-}\frac{1}{8}e^{5} - \frac{9}{8}e^{3} - \frac{3}{4}e$ |
| 41 | $[41, 41, 5w + 53]$ | $-\frac{1}{8}e^{5} + \frac{9}{8}e^{3} + \frac{3}{4}e$ |
| 67 | $[67, 67, w + 28]$ | $\phantom{-}\frac{3}{4}e^{4} - \frac{43}{4}e^{2} + \frac{47}{2}$ |
| 67 | $[67, 67, w + 39]$ | $\phantom{-}\frac{3}{4}e^{4} - \frac{43}{4}e^{2} + \frac{47}{2}$ |
| 71 | $[71, 71, 40w + 427]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{17}{4}e^{3} + \frac{33}{2}e$ |
| 71 | $[71, 71, 8w + 85]$ | $-\frac{1}{4}e^{5} + \frac{17}{4}e^{3} - \frac{33}{2}e$ |
| 73 | $[73, 73, -2w + 23]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{11}{2}e^{2} + 3$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $-1$ |